Doctor Who Social Club

My best suggestion is to just start with the 2005 reboot. Start with the Ninth Doctor. It was designed to be a starting place for new fans. And once you get into the show, it gets far less daunting. It's highly bingable. It's got that early 2000s flair of individual stories per episode, but with an overarching story just about every season that will pay off if you're paying attention enough to pick up on the details. Nine's run is short, but sweet. Then you move on to Ten, who I'm sure most people know as the fan favorite. His run is phenomenal and, although my favorite Doctor is Twelve and my favorite era is the Pond era (which is part of Eleven's run) I have to say that Ten's run is probably the best written.

If you're interested in going back to watch the classic stuff, watching "NuWho" will get you prepped for it so don't feel like you have to watch that first. Also, be aware that with Classic Who, you very much so can pick and choose what you want to watch. I'm not personally a huge fan of the First and Second Doctor's eras, but I adore Three, Four, and Five so I have seen far more of their stories than I have the other Classic doctors.

It's really up to you and your preferences, but that's my best suggestion. I mean, anytime there's a showrunner swap, the show kind of tends to get a minor reboot, so any of those times would be a decent one to jump in. But If you skip Nine and Ten and go straight to Eleven, you miss a lot of good storytelling. Same if you skip Eleven and Twelve and go straight for Thirteen. It's worth watching it all. And then if you're hungry for more, going back and checking out the classics.